Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Some properties of the HNBUE and HNWUE classes of life distributions
Umeå University, Faculty of Science and Technology, Mathematical statistics.
1980 (English)Report (Other academic)
Abstract [en]

The HNBUE (HNWUE) class of life distributions (i.e. for which f F (x)dx< (>)00 t< (>) y exp(-t/y) for t > 0, where y = / F(x)dx) is studied. We prove0that the HNBUE (HNWUE) class is larger than the NBUE (NWUE) class. We alsopresent some characterizations of the HNBUE (HNWUE) property by using theTotal Time on Test (TTT-) transform and the Laplace transform. Further weexamine whether the HNBUE (HNWUE) property is preserved under the reliabilityoperations (1) formation of coherent structure, (2) convolution and(3) mixture. Some bounds on the moments and on the survival function of aHNBUE (HNWUE) life distribution are also presented. The class of distributionswith the discrete HNBUE (discrete HNWUE) property (i.e. for which00 00 00I P. < (>) y(l-l/y)k for k = 0,1,2j=k J "where yi=0 JI p. and P. = E p, )J k=j+l kis also studied.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1980. , 48 p.
Series
Statistical research report, ISSN 0348-0399 ; 1980:8
Keyword [en]
Life distribution, survival function, survival probability, HNBUE, HNWUE, discrete HNBUE, discrete HNWUE, TTT-transform, Laplace transform, damage model, coherent structure, convolution, mixture
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-78994OAI: oai:DiVA.org:umu-78994DiVA: diva2:638402
Projects
digitalisering@umu
Note

There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.

Available from: 2013-07-30 Created: 2013-07-30 Last updated: 2013-07-30Bibliographically approved
In thesis
1. Properties and tests for some classes of life distributions
Open this publication in new window or tab >>Properties and tests for some classes of life distributions
1980 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

A life distribution and its survival function F = 1 - F with finitemean y = /q F(x)dx are said to be HNBUE (HNWUE) if F(x)dx < (>)U exp(-t/y) for t > 0. The major part of this thesis deals with the classof HNBUE (HNWUE) life distributions. We give different characterizationsof the HNBUE (HNWUE) property and present bounds on the moments and on thesurvival function F when this is HNBUE (HNWUE). We examine whether theHNBUE (HNWUE) property is preserved under some reliability operations andstudy some test statistics for testing exponentiality against the HNBUE(HNWUE) property.The HNBUE (HNWUE) property is studied in connection with shock models.Suppose that a device is subjected to shocks governed by a counting processN = {N(t): t > 0}. The probability that the device survives beyond t isthen00H(t) = S P(N(t)=k)P, ,k=0where P^ is the probability of surviving k shocks. We prove that His HNBUE (HNWUE) under different conditions on N and * ^orinstance we study the situation when the interarrivai times between shocksare independent and HNBUE (HNWUE).We also study the Pure Birth Shock Model, introduced by A-Hameed andProschan (1975), and prove that H is IFRA and DMRL under conditions whichdiffer from those used by A-Hameed and Proschan.Further we discuss relationships between the total time on test transformHp^(t) = /q ^F(s)ds , where F \t) = inf { x: F(x) > t}, and differentclasses of life distributions based on notions of aging. Guided by propertiesof we suggest test statistics for testing exponentiality agains t IFR,IFRA, NBUE, DMRL and heavy-tailedness. Different properties of these statisticsare studied.Finally, we discuss some bivariate extensions of the univariate properties NBU, NBUE, DMRL and HNBUE and study some of these in connection with bivariate shock models.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 1980. 16 p.
Keyword
Life distribution, survival function, exponential distribution, IFR, IFRA, NBUE, DMRL, HNBUE, shock model, total time on test transform, testing of exponentiality
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-78990 (URN)
Public defence
1980-10-17, Samhällsvetarhuset, hörsal D, Umeå universitet, Umeå, 09:15
Projects
digitalisering@umu
Note

There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.

Available from: 2013-07-30 Created: 2013-07-30 Last updated: 2013-07-30Bibliographically approved

Open Access in DiVA

Some properties of the HNBUE and HNWUE classes of life distributions(2382 kB)191 downloads
File information
File name FULLTEXT02.pdfFile size 2382 kBChecksum SHA-512
319e2a92a98c2f662d4bfa33e803719723587550300d72dad66042aecc9622813b3842f1e5cc64ac4a2989081befc76b0117f50a7954e4eb0288c7c062c74177
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Klefsjö, Bengt
By organisation
Mathematical statistics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 191 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 72 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf